The present invention relates to a fiber optic gyro of a zero serrodyne modulation system employing a linear phase ramp voltage.
There has been proposed a wide-dynamic-range, low-drift fiber optic gyro of the type having a biasing phase modulator and a ramp phase modulator connected to the one and the other end of an optical fiber coil, respectively. The biasing phase modulator and the ramp phase modulator each comprises a pair of electrodes formed in association with an optical waveguide. A biasing voltage and a ramp voltage are applied to the biasing phase modulator and the ramp phase modulator, respectively, to thereby provide a phase difference between two rays of light propagating through the optical fiber coil in opposite directions. The phase difference between the two rays of light which propagate through the optical fiber coil and interfere with each other is detected from the output of a photodetector. The detected output is used to control the polarity and frequency of the ramp voltage so that the phase difference may assume a predetermined value.
FIG. 1 shows an example of such a conventional fiber optic gyro of the zero serrodyne modulation system utilizing a linear ramp voltage.
Light 10 emitted from a light source 11 is provided via an optical coupler 13 and a polarizer 14 to an optical coupler 15, wherein it is split into two rays of light 5a and 5b. The one light 5a and the other light 5b are supplied to an optical fiber coil 17 at the one and the other end 17a and 17b thereof, respectively, and propagate therethrough as right-handed light and left-handed light. The two rays of light 7a and 7b having thus propagated through the optical fiber coil 17 are supplied therefrom at the ends 17b and 17a to the optical coupler 15, wherein they interfere with each other. The resulting interference light 9 is provided via the polarizer 14 and the optical coupler 13 to a photodetector 19 for conversion into an electric signal as in ordinary fiber optic gyros.
A biasing phase modulator 21 is disposed between the optical coupler 15 and the one end 17a of the optical fiber coil 17 and a ramp phase modulator 22 is disposed between the optical coupler 15 and the other end 17b of the optical fiber coil 17. A biasing voltage Bi is applied from a signal generator 30 to the biasing phase modulator 21 for phase shifting the light 5a to be supplied to the optical fiber coil 17 at the one end 17a thereof and the light 7b having propagated through the optical fiber coil 17 from the other end 17b thereof and to be supplied to the optical coupler 15. On the other hand, a ramp voltage Ra is applied from a ramp voltage generator 40 to the ramp phase modulator 22 for phase shifting the light 5b to be supplied to the optical fiber coil 17 at the other end 17b thereof and the light 7a having propagated through the optical fiber coil 17 from the one end 17a thereof and to be supplied to the optical coupler 15. The light 7a and the light 7b are combined by the optical coupler 15 into the interference light 9, which is provided to the photodetector 19. The output Va of the photodetector 19 is supplied to a phase difference detect/control unit 50, which detects from the detected output Va applied thereto the total phase difference .DELTA..phi. between the light 7a and the light 7b interfering with each other in the optical coupler 15 and outputs a voltage Ve corresponding to the detected phase difference .DELTA..phi.. The output Ve of the phase difference detect/control unit 50 is provided to the ramp voltage generator 40 to control the polarity and frequency of the ramp voltage Ra from the ramp voltage generator 40 so that the detected total phase difference .DELTA..phi. may reach a predetermined value. That is, the remainder which results from subtracting, from the phase difference .DELTA..phi., a phase difference .DELTA..phi..sub.B which is caused by the application of the biasing voltage Bi to the biasing phase modulator 21 is the sum .DELTA..phi..sub.0 of a Sagnac phase difference .DELTA..phi..sub.s which is caused by the application of an input angular rate .OMEGA. to the optical fiber coil 17 and a ramp phase difference .DELTA..phi..sub.r which is caused by the application of the ramp voltage Ra to the ramp phase modulator 22, that is, .DELTA..phi..sub.0 =.DELTA..phi..sub.s +.DELTA..phi..sub.r, and the polarity and frequency of the ramp voltage Ra is controlled so that the above-mentioned sum .DELTA..phi..sub.0 may be zero or an integral multiple of 2.pi.rad.--zero, in general.
The biasing voltage Bi is a sinusoidal or rectangular voltage of a frequency fm (=1/2.tau., where .tau. is the time necessary for the propagation of the two rays of lights 5a and 5b through the optical fiber coil 17). The phase modulation by the biasing phase modulator 21 supplied with such a biasing voltage is to set an operating point of the fiber optic gyro by providing the phase difference .DELTA..phi..sub.B of .+-..pi./2rad. between the two rays of light 7a and 7b which have propagated through the optical fiber coil 17 and interfere with each other. For example, where the biasing voltage Bi is a square voltage of an amplitude .+-.Vs, the light 5a which is subjected to a phase shift +.pi./4 (or -.pi./4) by the voltage +Vs (or -Vs) in the phase modulator 21 and is then applied to the optical fiber coil 17 is emitted therefrom as the light 7a after the lapse of time .tau.. On the other hand, when the light 5b entered the optical fiber coil 17 simultaneously with the light 5a is applied to the phase modulator 21 after the lapse of time .tau., the biasing voltage Bi has changed to -Vs (or +Vs), and hence the light 5b is subjected to a phase shift -.pi./4 (or +.pi./4), thereafter being output as the light 7b. Accordingly, the phase difference which is provided between the light 7a and the light 7b is +.pi./2 (or -.pi./2). The same is true of the case of employing a sinusoidal voltage.
The ramp voltage Ra goes positive or negative as depicted in FIG. 2. The phase modulation by the ramp phase modulator 22 supplied with such a ramp voltage provides the ramp phase difference .DELTA..phi..sub.r, which is a maximum of 2krad. (where k=.+-.1, .+-.2, ...), generally, up to .+-.2.pi.rad., between the two rays of light 7a and 7b which have propagated through the optical fiber coil 17 and interfere with each other. That is intended to cancel the Sagnac phase difference .DELTA..phi..sub.s so that sin(.DELTA..phi..sub.s +.DELTA..phi..sub.r)=0, as referred to previously.
The phase difference .DELTA..phi..sub.0 remaining after subtracting the phase difference .DELTA..phi..sub.B, which is caused by the application of the biasing voltage Bi to the biasing phase modulator 21, from the total phase difference .DELTA..phi. between the two rays of light 7a and 7b which interfere with each other in the optical coupler 15 is expressed as follows: ##EQU1## As is well-known in the art, the Sagnac phase difference .DELTA..phi..sub.s is given by ##EQU2## where R is the radius of the optical fiber coil 17, L is the length of the optical fiber coil 17, .lambda. is the wavelength of light 7a, 7b which propagates through the optical fiber coil 17, and C is the velocity of light in a vacuum.
In the ramp phase modulator 22 the light 5b which is supplied to the optical fiber coil 17 at its one end 17b is subjected to a phase shift .phi..sub.b corresponding to a value of the ramp voltage Ra at that time. These phase shifts .phi..sub.a and .phi..sub.b may hereinafter be referred to as ramp phase shifts and representatively denoted by .phi..sub.R. The light 5a which is input into the optical fiber coil 17 at the other end 17a is supplied via the one end 17b thereof, after the lapse of time .tau., to the ramp phase modulator 22, wherein it is subjected to a phase shift .phi..sub.a corresponding to a value of the ramp voltage Ra at that time. When the input angular rate .OMEGA. is applied clockwise and the Sagnac phase difference .DELTA..phi..sub.s goes negative, the ramp voltage Ra is controlled to be positive by the output Ve of the phase difference detect/control unit 50 as shown at the left-hand side in FIG. 2. In this instance, the phase shifts .phi..sub.a and .phi..sub.b bear such a relationship as shown at the left-hand side in FIG. 3. In consequence, the ramp phase difference .DELTA..phi..sub.r =.phi..sub.a -.phi..sub.b resulting from the application of the ramp voltage Ra to the ramp phase modulator 22 goes positive in a period Pa and negative in a period Pb as depicted at the left-hand side in FIG. 4. Where the input angular rate .OMEGA. is applied counterclockwise and the Sagnac phase difference .DELTA..phi..sub.s goes positive, the ramp voltage Ra is made negative by the output Ve of the phase difference detect/control unit 50 as shown at the right-hand side in FIG. 2 and the phase shifts .phi..sub.a and .phi..sub.b bear such a relationship as depicted at the right-hand side in FIG. 3. As a result of this, the ramp phase difference .DELTA..phi..sub.r goes negative in the period Pa and positive in the period Pb as shown at the right-hand side in FIG. 4.
Accordingly, as will be seen from FIG. 3, letting the period and frequency of the ramp voltage Ra be represented by T and f.sub.R, respectively, the ramp phase difference .DELTA..phi..sub.r indicated by the arrow becomes, in the period Pa, as follows: ##EQU3## Letting the refractive index of the optical fiber coil 17 be represented by n, the following relationship exists: ##EQU4## Hence, substitution of Eq. (4) into Eq. (3) gives the following equation: ##EQU5## By controlling the polarity and the frequency r.sub.R of the ramp VOltage Ra so that the phase difference .DELTA..phi..sub.0 expressed by Eq. (1) may be reduced to zero, that is, EQU .DELTA..phi..sub.r =-.DELTA..phi..sub.s ( 6)
the frequency f.sub.R is obtained from Eqs. (5) and (6) as follows: ##EQU6## Accordingly, the angular rate .OMEGA. applied to the optical fiber coil 17 is expressed as follows: ##EQU7## Whereas, in the case where the input angular rate .OMEGA. is applied clockwise, i.e. in the negative direction and the ramp voltage Ra goes positive, k becomes +1, and in the case where the input angular rate .OMEGA. is applied counterclockwise, i.e. in the positive direction and the ramp voltage Ra goes negative, k becomes -1. In this way, the direction and the magnitude of the input angular rate .OMEGA. can be measured from the polarity and the frequency f.sub.R of the ramp voltage Ra. Incidentally, the coefficient (kn.lambda./2R) in Eq. (8) is called a scale factor and is the measurement sensitivity that is expressed by an angular rate per cycle of the ramp voltage (.OMEGA./f.sub.R).
The ramp phase modulator 22 such as described in the foregoing usually includes optical waveguide formed as by diffusing titanium into an electro-optic crystal as of lithium niobate and a pair of electrodes for receiving a voltage for modulation. The ramp phase modulator 22 is connected in series to the other end 17b of the optical fiber coil 17. The amount of phase shift of the light in the phase modulator is proportional to the product, .gamma.Vp, of the electro-optic constant .gamma. of the electro-optic crystal and the applied voltage Vp. The electro-optic constant .gamma. is temperature-dependent and has a temperature coefficient of about 500 ppm/.degree. C. though it somewhat differs with the cutting direction of the electro-optic crystal. Consequently, the amount of phase shift of light in the phase modulator varies with temperature, even if the applied voltage Vp remains unchanged.
In the conventional fiber optic gyro described above in respect of FIG. 1 the peak-to-peak value or maximum amplitude of the ramp voltage Ra which is applied from the ramp voltage generator 40 to the ramp phase modulator 22 is set to such a fixed value that a maximum phase shift of light by the maximum amplitude may be 2k.pi.rad. at a specified temperature, say, 15.degree. C. However, in the case where the temperature of the fiber optic gyro and consequently the temperature of the ramp phase modulator 22 differs from the above-said specified temperature due to a change in ambient temperature, the electro-optic constant .gamma. of the electro-optic crystal forming the ramp phase modulator 22 changes accordingly, by which the maximum phase shift deviates from 2k.pi.rad., and consequently, the relationship between the input angular rate .OMEGA. and the frequency f.sub.R of the ramp voltage Ra deviates from the relationship defined by Eq. (7) or (8), resulting in a scale factor error in the output of the fiber optic gyro.
FIG. 5 shows measured values of the scale factor error in the conventional fiber optic gyro in which the peak value of the ramp voltage Ra was set such that the maximum phase shift at 15.degree. C. would be .+-.2.pi.rad. When the temperature of the fiber optic gyro is .+-.70.degree. C. relative to 15.degree. C., the maximum phase shift will deviate about .+-.3.5% from 2.pi.rad. and the scale factor error will be as large as .+-.0.13% or so.